Okay, to add to what has been previously answered, there are a couple of major details I need to point out.
1. If it's a black-and-white image, you need to check if it's been saved as "bitmap" "grayscale" or in color ("RGB" or "CMYK" Once you open it in Photoshop, notice the title bar for the image. In parentheses it will say one of those things. In order to use the magic wand it cannot be in "bitmap." You can change this by going to the "Image" menu and selecting "Mode" and then "grayscale" If it's already in "grayscale" or one of the color modes you're okay.
[I'll point out here that if you're importing it into another program, just make it "bitmap," save it as a TIFF and you'll be completely fine. It will be transparent automatically once you import it.]
2. Like they said, select all the background layer and copy/paste, which will create a new layer. You can then delete the background layer in the layers pallette.
3. The magic wand looks just like that. It's like a stick with little sparklies at the tip. Once you select the magic wand from the toolbox, you'll need to look at the top of the screen, where the tool options are. You should see a checkbox that says "contiquous." You want to have that checked. If you don't you'll end up selecting all the white space, both outside and inside, which may not be what you want. If you're just trying to get the space around it to be transparent, you want to check continquous.
4. Then click in the white space around the object. If the lines of the object hit the outside edges, you may not get all of it at once. There are two ways you can get around this.
a. change the canvas size. "Image" menu, "Canvas Size..." and add just .1 inch on every size. Make sure you select the middle square so it addes that .1 inch all around. Then try the magic wand.
or
b. Select all the surrounding white space by holding down the Shift Key during the selection with the magic wand.
Then delete.
5. Flatten the image using the layers pallette (the little arrow at the top right of the layers pallette reveals a popup menu)
6. Save as a gif.